In the process of helping a nephew (2011, math/geometry teacher), we began chasing embedded geometries (tetrahedron and octahedron cluster) by dividing the edges by 2 and connecting those new vertices. In 45 steps we were down into the CERN-scale. In another 67 steps within, we were down into the Planck scale.

We learned a little about base-2 exponentiation. Then starting with our little cluster, we multiplied by 2 and in about 90 steps (total of 202 notations), we were out to the age and size of the universe.

We thought it was a neat, home-grown, STEM tool until we began thinking about those first 64 notations in light of the rather remarkable Wheat & Chessboard story! In reviewing the emerging literature of the infinitesimally small, everything from strings, pions, and quarks, to topos theory, Langlands conjectures, and so on, it seemed that this rather extraordinary place for “mathematical purity” (that’s my euphemistic expression) was not being respected for its potential diversity and complexity.